In mechanics, the conversation starts with static discussions such as forces. Quickly, though, the necessity for the study of movement leads to a definition of work. The conservative nature of the electric field allows for quick application of the mechanical concept of work to electric problems concerning work, energy, velocity and displacement.

A particle with charge \(q = -6\mu \text{C}\) moves from (0 \(\text{m}\), 0 \(\text{m}\)) to (1 \(\text{m}\), 2 \(\text{m}\)) in a region with electric field \(\vec{E}=(7.0 \frac{\text{N}}{\text{C}}) \hat{x}\). Find the work done by the electric field.

Solution: Use the theorem that says the work done by the electric field is \(W=qEd_{\parallel}\). Since the electric field points in the x direction, the parallel displacement is just \(d_\parallel=\Delta x = x_f - x_0 = 1 - 0 = 1 \text{m}\).

A bumble bee charged to \(1 \text{ C}\) flies from \((0 \text{ m}, 0\text{ m}) \) to \((1 \text{ m}, 1\text{ m})\) through a region with electric field \(\vec{E}=(\hat{x}+\hat{y})\dfrac{N}{C}\). Find the work done by the electric field on the bumble bee.